Parliament Square can be a harsh place. On the eastern side of its stately traffic island, where Brian Haw spent most of the last 10 years, there is no shade. There is no protection from wind or rain, apart from the small battered protesters' tents that cling to the pavement; and it is hard to protest effectively from inside a zipped-up tent. Traffic roars past, day and night, inches away. And after dark, when the pavement turns cold as a tombstone, drinkers from nearby pubs sometimes pay the Parliament Square peace campaigners a visit. The ensuing discussions about British foreign policy, and the right of Haw and the others to criticise it so visibly, have not always been pretty.

During his time in the square, Haw, who died from lung cancer at the weekend, aged rapidly. His face grew more lined, his movements stiffer. Towards the end of his life, he would often just sit, staring in the direction of parliament, like a sort of political living sculpture. Behind him were spread his weatherbeaten placards and banners: "Iraq 2,000,000 dead 4,000,000 fled," read one that was still there yesterday, as Haw's small band of helpers talked reverently about him to a steady trickle of reporters. "Genocide. Theft. Torture. Cholera. Starvation." More confrontational still, and generally less closely examined by visitors to his peace encampment, was his display of fading photographs of maimed and deformed Iraqi children. An adjacent placard sought to explain: "Depleted Uranium Munitions. Our War Material. Our Shame! USA/UK Target [and] Nuke Babies. War Crime!"

The longer Haw protested, and the longer Britain's wars in Iraq and Afghanistan dragged on and lost credibility, the more he attracted admiration, grudging and otherwise. Channel 4 dubbed him the Most Inspiring Political Figure of 2007. Boris Johnson, before he became mayor of London, wrote in the Daily Telegraph in 2006: "Brian Haw, the father of seven, anti-war loony who used to bellow at me on my bicycle . . . I thought his posters and general gubbins were a disgrace and spoiled the look of the place; and yet he . . . represented something dementedly British . . . Across the world, Britain still stands for a certain idea of liberty, a particular concept of the relationship between the citizen and the state."

Yesterday, as always, many of the tourists who had come to see the Houses of Parliament, after exiting Westminster tube station, stopped first to take photos of Haw's banners. In these austere times, protesters' encampments outside parliaments are no longer so rare, but Haw's is one of the world's most famous and longest-running. How uncomfortable that must be for the many MPs who have voted so unquestioningly for every recent war plan put before them. The Commons, in recent decades, has not been good at representing the large minority of Britons who oppose most wars, with only tiny handfuls of MPs daring to defy our bellicose prime ministers and the newspaper bombardiers. Haw did something to redress that imbalance.

At regular intervals, British politicians, including Johnson (as mayor), Labour and Conservative MPs, the Greater London Authority and Westminster council, tried and failed to remove Haw and the other Parliament Square activists who accumulated like barnacles around him. To many of the official users and custodians of the square, freedom of speech seemed to count for less than the look of the place – and this exasperation at Haw often seemed at its strongest in the run-up to royal visits to Westminster. A country's attitude to political behaviour in its most famous public spaces is always revealing.

Yet at other times Haw was ignored by Westminster insiders – his seeming permanence making him as easy to blank out, perhaps, as all the other Westminster statues. Last year, when I was attending the Chilcot inquiry into the Iraq war, which was being held only a couple of hundred yards away, I used one of the breaks in the rather bloodless hearings to walk over to Haw's encampment and remind myself of the horrors and furious opposition the war had generated – and maybe get a bit of useful colour. Haw was there, pacing in the snow in inadequate-looking clothes. But none of the numerous other Chilcot journalists had come to see him.

Some of this was probably Haw's own fault. He was hardly a crank, but he had something of the street-corner evangelist about him. His obsessiveness could be alienating, or lead him down dubious pathways. On his website, he denounced the other peace campaigners in the square who were not part of his campaign and had arrived there after him as government "agent provocateurs", deployed, he alleged, to discredit him and create additional grounds for his removal. Sometimes there were late-night confrontations. When I wrote about this separate group of activists last year, carefully including Haw's allegations against them and their denials, his website denounced me too.

But anyone who has spent a decade protesting on the same stretch of pavement and grass is probably entitled to be intemperate and territorial. In Westminster, especially today's Westminster of ever-spreading roadblocks and ever-higher security fences and ever more elaborate security checks and ominously polite armed policemen, street protests – whether by leftwing students or rightwing hunt enthusiasts – are never welcome for long. At best, demonstrators may occupy Parliament Square for a few hours before the police horses come thundering in.

Haw created a precedent for a different kind of Westminster: messier, noisier, more crudely and visibly politicised, with the consequences of some of the British government's actions abroad not swept under the carpet, or examined by Whitehall connoisseurs in small, slightly soporific rooms, as at Chilcot, but in plain view of all London and its visitors, 24/7. Many MPs don't like this new Westminster, and will be secretly, or not so secretly, hoping that Haw's death marks the beginning of the return of Parliament Square to empty splendour. With Haw gone, I suspect the days of the Westminster peace camp may be numbered. But I also suspect there are some anti-cuts protesters taking an interest in how he managed to stay there for so long.